New to mortgages but think I'm ready

I'm in the service industry and work full time as a bartender and bar manager, title is glorified but I have it.

The details:

At current position for 3.5 years, and it great standing with the small group of restaurants

On paper I bring in ~50k a year based on tax returns. Realistically its closer to 80k.

EX Fico is 727.

Monthly debts:

- Car loan: 310

- Credit cards, I pay in full so I can pay them off and use debit if needed

- Student loans, monthly payment is 230, but I have been putting 600/mo towards them. 3,000 remaining and can pay it off tomorrow

- House keeper in my dads house and pay rent to him, but more or less off the books.

If I pay my student loans, my DTI is maybe 7-8%

Now the hard part since I deposit cash all the time and it doesn't match my paycheck. I do have an account with ~13,400 that hasn't had anything added for 2 months. I have $2500 in checking that pretty much hovers around that amount as cash comes in and debts get paid. Have 21k in liquid assets in stocks.

Thinking that I will only use the 13.4k if possible as the down payment as the deposits are 2 months old, from what I've read that's the timeframe that the banks won't ask where the deposits came from.

Wondering if I could get preapproved and if so, roughly for how much. My girlfriend would be living with me and paying towards the mortgage but her DTI is too high to put her on it.

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Many factors affect your FICO Scores and the interest rates you may receive. Fair Isaac is not a credit repair organization as defined under federal or state law, including the Credit Repair Organizations Act. Fair Isaac does not provide "credit repair" services or advice or assistance regarding "rebuilding" or "improving" your credit record, credit history or credit rating.
FTC's website on credit.

IMPORTANT INFORMATION: All FICO® Score products made available on myFICO.com include a FICO® Score 8, along with additional FICO® Score versions. Your lender or insurer may use a different FICO® Score than the versions you receive from myFICO, or another type of credit score altogether. Learn more

FICO, myFICO, Score Watch, The score lenders use, and The Score That Matters are trademarks or registered trademarks of Fair Isaac Corporation. Equifax Credit Report is a trademark of Equifax, Inc. and its affiliated companies. Many factors affect your FICO Score and the interest rates you may receive. Fair Isaac is not a credit repair organization as defined under federal or state law, including the Credit Repair Organizations Act. Fair Isaac does not provide "credit repair" services or advice or assistance regarding "rebuilding" or "improving" your credit record, credit history or credit rating. FTC's website on credit.